贝叶斯L2型TSK模糊系统

针对传统Takagi-Sugeno-Kan(TSK)模糊系统处理大规模数据时间代价较高的问题,提出一种基于概率模型框架的L2型TSK模糊系统建模策略,建立具有处理大规模数据能力的贝叶斯L2型TSK模糊系统(B-TSK-FS).具体地,基于L2型TSK模糊系统的输出误差概率化表示,对系统前后件参数联合学习,提高系统的泛化能力.另外,引入狄利克雷先验分布函数,对模糊隶属度稀疏化表示,实现样本的压缩,降低运算时间.在模拟和真实数据集上的实验结果验证了所提出模糊系统的优势.     

基于模糊子空间聚类的0 阶岭回归TSK 模糊系统

经典数据驱动型TSK模糊系统在利用高维数据训练模型时,由于规则前件采用的特征过多,导致规则的解释性和简洁性下降.对此,根据模糊子空间聚类算法的子空间特性,为TSK模型添加特征抽取机制,并进一步利用岭回归实现后件的学习,提出一种基于模糊子空间聚类的0阶岭回归TSK模型构建方法.该方法不仅能为规则抽取出重要子空间特征,而且可为不同规则抽取不同的特征.在模拟和真实数据集上的实验结果验证了所提出方法的优势.     

结构辨识和参数优化协同学习的概率TSK模糊系统

传统Takagi-Sugeno-Kang(TSK)模糊系统的结构辨识和参数优化往往分阶段进行,同时模糊规则数需要预先设定,因此TSK模糊系统的逼近性能和解释性往往不理想.针对此问题,提出了一种结构辨识和参数优化协同学习的概率TSK模糊系统(Probabilistic TSK fuzzy system,PTSK).首先,...     

具有强解释性的贝叶斯MA型模糊系统

提出用于规则前件学习的中心点交叉涌现的大间隔贝叶斯模糊聚类(CECLM-BFC)算法.考虑不同样本间聚类中心的排斥作用使得聚类中心间距最大化,并采用粒子滤波方法在不同类别样本中交替执行,自动求解出最优聚类结果,包括聚类数、模糊隶属度和聚类中心.在模糊规则后件参数学习上使用分类面大间隔的策略,以MA型模糊系统为研究对象构造具有强解释性的贝叶斯MA型模糊系统(BMA-FS).实验结果表明,BMA-FS能够取得令人满意的分类性能,且模糊规则具有高度的解释性.     

单趟贝叶斯模糊聚类算法

对于概率模糊聚类,贝叶斯模糊聚类方法表现出良好的聚类性能,它从先验知识和贝叶斯理论的角度出发,采用最大后验概率理论处理模糊划分,进而获取最终的聚类结果.该方法有效地结合了概率论和模糊论两者的优点,较之传统的模糊聚类算法（如FCM算法）,该方法能够获取全局最优解并估计聚类个数.但在大数据时代,该方法较高的时间复杂度限制了它的实用性.针对此问题,首先在贝叶斯模糊聚类中引入加权机制,提出了加权贝叶斯模糊聚类算法;然后将其与单趟聚类框架相结合,提出了面向大规模数据的快速单趟贝叶斯模糊聚类算法,并从理论上对相关性质进行了较为深入的分析.所提出的单趟贝叶斯模糊聚类新算法较之贝叶斯模糊聚类算法在时间复杂度和收敛性上均有着不同程度的性能提升,同时继承了贝叶斯模糊聚类的良好的聚类性能.最后,相关实验结果亦验证了所提方法的有效性.     

适合大规模数据集且基于LLM的0阶TSK模糊分类器

针对传统分类器的泛化性能差、可解释性及学习效率低等问题, 提出0阶TSK-FC模糊分类器.为了将该分类器 应用到大规模数据的分类中, 提出增量式0阶TSK-IFC模糊分类器, 采用增量式模糊聚类算 法(IFCM($c+p$))训练模糊规则参数并通过适当的矩阵变换提升参数学习效率.仿真实验表明, 与FCPM-IRLS模糊分类器、径向基函数神经网 络相比, 所提出的模糊分类器在不同规模数据集中均能保持很好的性能, 且TSK-IFC模糊分类器在大规模数据分类中尤为突出.     

A new approach to fuzzy modeling of nonlinear dynamic systems with noise: relevance vector learning mechanism

This paper presents a new fuzzy inference system for modeling of nonlinear dynamic systems based on input and output data with measurement noise. The proposed fuzzy system has a number of fuzzy rules and parameter values of membership functions which are automatically generated using the extended relevance vector machine (RVM). The RVM has a probabilistic Bayesian learning framework and has good generalization capability. The RVM consists of the sum of product of weight and kernel function which projects input space into high dimensional feature space. The structure of proposed fuzzy system is same as that of the Takagi-Sugeno fuzzy model. However, in the proposed method, the number of fuzzy rules can be reduced under the process of optimizing a marginal likelihood by adjusting parameter values of kernel functions using the gradient ascent method. After a fuzzy system is determined, coefficients in consequent part are found by the least square method. Examples illustrate effectiveness of the proposed new fuzzy inference system.     

基于训练空间重构的多模块TSK模糊系统

利用重构训练样本空间的手段,提出一种多训练模块Takagi-Sugeno-Kang （TSK）模糊分类器H-TSK-FS.它具有良好的分类性能和较高的可解释性,可以解决现有层次模糊分类器中间层输出和模糊规则难以解释的难题.为了实现良好的分类性能,H-TSK-FS由多个优化零阶TSK模糊分类器组成.这些零阶TSK模糊分类器内部采用一种巧妙的训练方式.原始训练样本、上一层训练样本中的部分样本点以及所有已训练层中最逼近真实值的部分决策信息均被投影到当前层训练模块中,并构成其输入空间.通过这种训练方式,前层的训练结果对后层的训练起到引导和控制作用.这种随机选取样本点、在一定范围内随机选取训练特征的手段可以打开原始输入空间的流形结构,保证较好或相当的分类性能.另外,该研究主要针对少量样本点且训练特征数不是很大的数据集.在设计每个训练模块时采用极限学习机获取模糊规则后件参数.对于每个中间训练层,采用短规则表达知识.每条模糊规则则通过约束方式确定不固定的输入特征以及高斯隶属函数,目的是保证所选输入特征具有高可解释性.真实数据集和应用案例实验结果表明,H-TSK-FS具有良好的分类性能和高可解释性.     

A two-stage evolutionary process for designing TSK fuzzy rule-basedsystems

Nowadays, fuzzy rule-based systems are successfully applied to many different real-world problems. Unfortunately, relatively few well-structured methodologies exist for designing and, in many cases, human experts are not able to express the knowledge needed to solve the problem in the form of fuzzy rules. Takagi-Sugeno-Kang (TSK) fuzzy rule-based systems were enunciated in order to solve this design problem because they are usually identified using numerical data. In this paper we present a two-stage evolutionary process for designing TSK fuzzy rule-based systems from examples combining a generation stage based on a (mu, lambda)-evolution strategy, in which the fuzzy rules with different consequents compete among themselves to form part of a preliminary knowledge base, and a refinement stage in which both the antecedent and consequent parts of the fuzzy rules in this previous knowledge base are adapted by a hybrid evolutionary process composed of a genetic algorithm and an evolution strategy to obtain the final Knowledge base whose rules cooperate in the best possible way. Some aspects make this process different from others proposed until now: the design problem is addressed in two different stages, the use of an angular coding of the consequent parameters that allows us to search across the whole space of possible solutions, and the use of the available knowledge about the system under identification to generate the initial populations of the Evolutionary Algorithms that causes the search process to obtain good solutions more quickly. The performance of the method proposed is shown by solving two different problems: the fuzzy modeling of some three-dimensional surfaces and the computing of the maintenance costs of electrical medium line in Spanish towns. Results obtained are compared with other kind of techniques, evolutionary learning processes to design TSK and Mamdani-type fuzzy rule-based systems in the first case, and classical regression and neural modeling in the second.     

Artificial Neural Networks are Zero-Order TSK Fuzzy Systems

In this paper, the functional equivalence between the action of a multilayered feed-forward artificial neural network (NN) and the performance of a system based on zero-order TSK fuzzy rules is proven. The resulting zero-order TSK fuzzy systems have the two following features: (A) the product t-norm is used to add IF-part fuzzy propositions of the obtained rules and (B) their inputs are the same as the initial neural networkNN ones. This fact makes us gain an understanding of the ANN-embedded knowledge. Besides, it allows us to simplify the architecture of a network through the reduction of fuzzy propositions in its equivalent zero-order TSK system. These advantages are the result of applying fuzzy system area properties on the neural networkNN area. They are illustrated with several examples.     

Application of type-2 neuro-fuzzy modeling in stock price prediction

We present an application of type-2 neuro-fuzzy modeling to stock price prediction based on a given set of training data. Type-2 fuzzy rules can be generated automatically by a self-constructing clustering method and the obtained type-2 fuzzy rules cab be refined by a hybrid learning algorithm. The given training data set is partitioned into clusters through input-similarity and output-similarity tests, and a type-2 TSK rule is derived from each cluster to form a fuzzy rule base. Then the antecedent and consequent parameters associated with the rules are refined by particle swarm optimization and least squares estimation. Experimental results, obtained by running on several datasets taken from TAIEX and NASDAQ, demonstrate the effectiveness of the type-2 neuro-fuzzy modeling approach in stock price prediction.     

用于不平衡数据分类的0阶TSK型模糊系统

处理不平衡数据分类时,传统模糊系统对少数类样本识别率较低.针对这一问题,首先,在前件参数学习上,提出了竞争贝叶斯模糊聚类（Bayesian fuzzy clustering based on competitive learning,BFCCL）算法,BFCCL算法考虑不同类别样本聚类中心间的排斥作用,采用交替迭代的执行方式并通过马尔科夫蒙特卡洛方法获得模型参数最优解.其次,在后件参数学习上,基于大间隔的策略并通过参数调节使得少数类到分类面的距离大于多数类到分类面的距离,该方法能有效纠正分类面的偏移.基于上述思想以0阶TSK型模糊系统为具体研究对象构造了适用于不平衡数据分类问题的0阶TSK型模糊系统（0-TSK-IDC）.人工和真实医学数据集实验结果表明,0-TSK-IDC在不平衡数据分类问题中对少数类和多数类均具有较高的识别率,且具有良好的鲁棒性和可解释性.     

A neuro-fuzzy inference system through integration of fuzzy logic and extreme learning machines.

This paper investigates the feasibility of applying a relatively novel neural network technique, i.e., extreme learning machine (ELM), to realize a neuro-fuzzy Takagi-Sugeno-Kang (TSK) fuzzy inference system. The proposed method is an improved version of the regular neuro-fuzzy TSK fuzzy inference system. For the proposed method, first, the data that are processed are grouped by the k-means clustering method. The membership of arbitrary input for each fuzzy rule is then derived through an ELM, followed by a normalization method. At the same time, the consequent part of the fuzzy rules is obtained by multiple ELMs. At last, the approximate prediction value is determined by a weight computation scheme. For the ELM-based TSK fuzzy inference system, two extensions are also proposed to improve its accuracy. The proposed methods can avoid the curse of dimensionality that is encountered in backpropagation and hybrid adaptive neuro-fuzzy inference system (ANFIS) methods. Moreover, the proposed methods have a competitive performance in training time and accuracy compared to three ANFIS methods.     

Online identification of evolving Takagi–Sugeno–Kang fuzzy models for crane systems

This paper suggests new evolving Takagi–Sugeno–Kang (TSK) fuzzy models dedicated to crane systems. A set of evolving TSK fuzzy models with different numbers of inputs are derived by the novel relatively simple and transparent implementation of an online identification algorithm. An input selection algorithm to guide modeling is proposed on the basis of ranking the inputs according to their important factors after the first step of the online identification algorithm. The online identification algorithm offers rule bases and parameters which continuously evolve by adding new rules with more summarization power and by modifying existing rules and parameters. The potentials of new data points are used with this regard. The algorithm is applied in the framework of the pendulum–crane system laboratory equipment. The evolving TSK fuzzy models are tested against the experimental data and a comparison with other TSK fuzzy models and modeling approaches is carried out. The comparison points out that the proposed evolving TSK fuzzy models are simple and consistent with both training data and testing data and that these models outperform other TSK fuzzy models.     

A Hybrid Learning Method for the Data-Driven Design of Linguistic Dynamic Systems

In lots of data based prediction or modeling applications, uncertainties and/or noises in the observed data cannot be avoided. In such cases, it is more preferable and reasonable to provide linguistic (fuzzy) predicted results described by fuzzy memberships or fuzzy sets instead of the crisp estimates depicted by numbers. Linguistic dynamic system (LDS) provides a powerful tool for yielding linguistic (fuzzy) results. However, it is still difficult to construct LDS models from observed data. To solve this issue, this paper first presents a simplified LDS whose inputoutput mapping can be determined by closed-form formulas. Then, a hybrid learning method is proposed to construct the data-driven LDS model. The proposed hybrid learning method firstly generates fuzzy rules by the subtractive clustering method, then carries out further optimization of centers of the consequent triangular fuzzy sets in the fuzzy rules, and finally adopts multiobjective optimization algorithm to determine the left and right end-points of the consequent triangular fuzzy sets. The proposed approach is successfully applied to three real-world prediction applications which are: prediction of energy consumption of a building, forecasting of the traffic flow, and prediction of the wind speed. Simulation results show that the uncertainties in the data can be effectively captured by the linguistic (fuzzy) estimates. It can also be extended to some other prediction or modeling problems, in which observed data have high levels of uncertainties.      

任务间共享和特有结构分解的多任务TSK模糊系统建模

现有的多任务Takagi-Sugeno-Kang (TSK) 模糊建模方法更注重利用任务间的相关性信息,而忽略了单个任务的特殊性。针对此问题,本文提出了一种考虑所有任务之间的共享结构和特有结构的TSK模糊系统多任务建模新方法。该方法将后件参数分解为共享参数和特有参数两个分量,既充分利用了任务间共享信息,又有效地保留了单个任务的特性。最后,本文利用增广拉格朗日乘子法(ALM)求解该最优化问题。实验结果表明,该方法比现有的模型获得了更好的表现。     

Chaotic time series prediction via artificial neural square fuzzy inference system

The present article investigates the application of second order TSK (Takagi Sugeno Kang) fuzzy systems in predicting chaotic time series. A method has been introduced for training second order TSK fuzzy systems using ANFIS (Artificial Neural Fuzzy Inference System) training method. In a second order TSK system existence of nonlinear terms in the rules’ consequence prohibits use of current available ANFIS codes as is but the proposed method makes it possible to use ANFIS for a class of simplified second order TSK systems. The main impact of this method on the expert and intelligent systems is to provide a new way for modeling and predicting the future situation of more complex phenomena with a smaller decision rule base. The most significance of the proposed method is the simplicity and available code reuse property. As a case study the proposed method is used for the prediction of chaotic time series. Error comparison shows that the proposed method trains the second order TSK system more effectively.     

Massively Parallel Probabilistic Reasoning with Boltzmann Machines

We present a method for mapping a given Bayesian network to a Boltzmann machine architecture, in the sense that the the updating process of the resulting Boltzmann machine model probably converges to a state which can be mapped back to a maximum a posteriori (MAP) probability state in the probability distribution represented by the Bayesian network. The Boltzmann machine model can be implemented efficiently on massively parallel hardware, since the resulting structure can be divided into two separate clusters where all the nodes in one cluster can be updated simultaneously. This means that the proposed mapping can be used for providing Bayesian network models with a massively parallel probabilistic reasoning module, capable of finding the MAP states in a computationally efficient manner. From the neural network point of view, the mapping from a Bayesian network to a Boltzmann machine can be seen as a method for automatically determining the structure and the connection weights of a Boltzmann machine by incorporating high-level, probabilistic information directly into the neural network architecture, without recourse to a time-consuming and unreliable learning process.     

A Self-Evolving Interval Type-2 Fuzzy Neural Network With Online Structure and Parameter Learning

This paper proposes a self-evolving interval type-2 fuzzy neural network (SEIT2FNN) with online structure and parameter learning. The antecedent parts in each fuzzy rule of the SEIT2FNN are interval type-2 fuzzy sets and the fuzzy rules are of the Takagi–Sugeno–Kang (TSK) type. The initial rule base in the SEIT2FNN is empty, and the online clustering method is proposed to generate fuzzy rules that flexibly partition the input space. To avoid generating highly overlapping fuzzy sets in each input variable, an efficient fuzzy set reduction method is also proposed. This method independently determines whether a corresponding fuzzy set should be generated in each input variable when a new fuzzy rule is generated. For parameter learning, the consequent part parameters are tuned by the rule-ordered Kalman filter algorithm for high-accuracy learning performance. Detailed learning equations on applying the rule-ordered Kalman filter algorithm to the SEIT2FNN consequent part learning, with rules being generated online, are derived. The antecedent part parameters are learned by gradient descent algorithms. The SEIT2FNN is applied to simulations on nonlinear plant modeling, adaptive noise cancellation, and chaotic signal prediction. Comparisons with other type-1 and type-2 fuzzy systems in these examples verify the performance of the SEIT2FNN.      

Robust TSK fuzzy modeling for function approximation with outliers

The Takagi-Sugeno-Kang (TSK) type of fuzzy models has attracted a great attention of the fuzzy modeling community due to their good performance in various applications. Most approaches for modeling TSK fuzzy rules define their fuzzy subspaces based on the idea of training data being close enough instead of having similar functions. Besides, training data sets algorithms often contain outliers, which seriously affect least-square error minimization clustering and learning algorithms. A robust TSK fuzzy modeling approach is presented. In the approach, a clustering algorithm termed as robust fuzzy regression agglomeration (RFRA) is proposed to define fuzzy subspaces in a fuzzy regression manner with robust capability against outliers. To obtain a more precision model, a robust fine-tuning algorithm is then employed. Various examples are used to verify the effectiveness of the proposed approach. From the simulation results, the proposed robust TSK fuzzy modeling indeed showed superior performance over other approaches